Method for determining a spatial distribution of the  permeability of an electrode of an electrochemical cell

ABSTRACT

The invention relates to a method for determining a spatial distribution (k x,y   f ) of a parameter of interest (k) representative of a permeability of a diffusion layer of at least one electrode of an electrochemical cell, comprising steps in which a spatial distribution (k x,y   f ) of the parameter of interest (k) is determined depending on the spatial distribution (Q x,y   e ) of a second thermal quantity (Q e ) estimated beforehand from the spatial distribution (T x,y   c ) of a set-point temperature (T c ) and from the spatial distribution (D x,y   r ) of a first thermal quantity (D r ).

TECHNICAL FIELD

The technical field of the invention is that of electrochemical reactors including a stack of electrochemical cells, such as fuel cells and electrolyzers, and more precisely that of methods for determining a parameter representative of the permeability of at least one electrode of the electrochemical cell, and that of methods for producing an electrochemical-cell electrode.

STATE OF THE PRIOR ART

An electrochemical reactor such as a fuel cell or electrolyzer conventionally includes a stack of electrochemical cells that each comprise an anode and a cathode that are electrically separated from each other by an electrolyte, an electrochemical reaction taking place in each cell between two reactants that are continuously fed thereto. In the case of a hydrogen fuel cell, the fuel (hydrogen) is brought into contact with the anode, whereas the oxidant (oxygen), which is for example contained in air, is brought into contact with the cathode. The electrochemical reaction is subdivided into two half reactions, an oxidation reaction and a reduction reaction, which take place at the anode/electrolyte interface and at the cathode/electrolyte interface, respectively. To take place, the electrochemical reaction requires the presence of an ionic conductor between the two electrodes, namely the electrolyte, which is optionally contained in a polymer membrane, and an electronic conductor formed by the external electric circuit. The stack of cells is thus the site of the electrochemical reaction: the reactants must be supplied thereto and the products and any unreactive species must be removed therefrom, as must the heat produced during the reaction.

The cells are conventionally separated from one another by bipolar plates that ensure the electrical interconnection of the cells. The plates include a circuit for distributing fuel, formed on an anodic side, and a circuit for distributing oxidant, formed on a cathodic side opposite the anodic side. Each distributing circuit often takes the form of a network of channels for example arranged in parallel or in a serpentine arrangement, said channels being suitable for bringing the reactive species uniformly to the corresponding electrode. The bipolar plates may also include a cooling circuit formed from a network of internal ducts that allow a head-transfer fluid to flow and thus the heat produced locally during the reaction in the cell to be removed.

Each electrode is conventionally formed from an active layer and a diffusion layer. The active layer, which is located between the electrolytic membrane and the diffusion layer, is the site of the electrochemical reaction. It generally includes a catalyst, for example platinum particles, placed on an electrically conductive and for example carbon-containing support, and an ionomer ensuring the protonic conductivity, Nafion for example. The diffusion layer is located between the active layer and the corresponding bipolar plate. It is produced from a porous material allowing gaseous reactive species to diffuse as far as the active layer and products generated by the electrochemical reaction to diffuse out. The diffusion layer has a given porosity φ that defines its permeability k, the latter representing the capacity of the layer to let a fluid pass through under the effect of a pressure gradient.

Conventionally, it is sought to preserve the lifetime of electrochemical cells, for example by increasing the uniformity of the spatial distribution of the current density exchanged by the cell in operation. Specifically, spatial nonuniformities in current density lead to spatial nonuniformities in the temperature of the cell, which may lead, on the one hand, to an increase in the rate of the degradation reactions of the various components of the cell, and on the other hand, to the generation of mechanical stresses of thermal origin that are liable to decrease the mechanical strength of the components of the cell.

With the aim of preserving the lifetime of an electrochemical cell, document FR2976732 describes a method for producing an electrochemical cell allowing uniform local heating to be obtained within the cell in operation. This heating depends on the electrical current density at each point of the cell, which is itself dependent on the partial pressure of the reactive species. Specifically, considering here the cathodic side of the cell, the amount of oxygen contained in the gas flowing through the distributing circuit gradually decreases as the oxygen is consumed by the cell, thereby leading to a spatial variation in the electrical current density produced by the cell, and therefore to a spatial variation in the heating of the cell. To prevent this spatial nonuniformity in the heating of the cell, the electrical conductivity between the bipolar plate delivering the oxygen and the cell is adjusted locally so as to compensate for the decrease in oxygen partial pressure.

In document WO2007/032903, the lifetime of an electrochemical cell is preserved by using an active layer the spatial distribution of the catalytic activity of which allows a uniform spatial distribution of current density to be obtained, which, in return, results in a uniform spatial distribution of the temperature of the cell in operation. In particular, this document describes a spatial distribution of catalytic activity that varies between the inlet and outlet of the circuits for distributing reactive species.

DISCLOSURE OF THE INVENTION

The objective of the invention is to remedy at least some of the drawbacks of the prior art, and more particularly to provide a method for determining the spatial distribution of a parameter representative of the permeability of an electrochemical-cell electrode especially allowing the uniformity of the local temperature of the electrochemical cell in operation to be increased and thus the lifetime of the latter to be preserved.

For this purpose, the invention provides a method for determining a spatial distribution of a parameter of interest representative of a permeability of a diffusion layer of at least one electrode of an electrochemical cell, said cell including two electrodes separated from each other by an electrolyte and placed between two bipolar plates suitable for bringing reactive species to the electrodes and for removing the heat produced by the cell in operation, at least one electrode including a diffusion layer suitable for ensuring the diffusion of a reactive species as far as the electrolyte, said method comprising the following steps:

-   i) providing an electrochemical cell, within which the parameter of     interest is distributed with an initial spatial distribution and for     which the spatial distribution of a temperature within the     electrochemical cell in operation has at least one local value     higher than or equal to a preset maximum local value; -   ii) defining a spatial distribution of a set-point temperature     within said electrochemical cell in operation, said distribution     being such that the local temperature values are lower than preset     maximum local values; -   iii) measuring a spatial distribution of a first thermal quantity     representative of the removal of heat within said electrochemical     cell in operation; -   iv) estimating a spatial distribution of a second thermal quantity     representative of the local production of heat within said     electrochemical cell in operation, depending on said spatial     distribution of the set-point temperature and on said measured     spatial distribution of the first thermal quantity, so that the     spatial distribution of the temperature of said electrochemical cell     in operation, the first thermal quantity of which cell having said     measured spatial distribution and the second thermal quantity of     which cell having said estimated spatial distribution, is     substantially equal to that of the set-point temperature; and -   v) determining a spatial distribution of the parameter of interest     depending on the estimated spatial distribution of the second     thermal quantity.

Thus, a spatial distribution of the parameter of interest is obtained and taking into account this spatial distribution in the considered electrochemical cell makes it possible to ensure that the latter has, in operation, a spatial distribution of temperature corresponding substantially to that of the set-point temperature. Thus, in operation the electrochemical cell then does not present zones in which the temperature is locally above preset maximum local values.

Here, the permeability corresponds to the permeability through the plane of the diffusion layer and not to the permeability in the plane of the layer.

The supply of the electrochemical cell may include a phase of experimentally prototyping or numerically modeling an electrochemical cell, a phase of measuring the spatial distribution of the temperature within the electrochemical cell in operation, then a phase of comparing the measured spatial distribution of the temperature to a preset spatial distribution of a maximum temperature. The local values of this spatial distribution of maximum temperature are the what are called preset maximum local values. When at least one local value of the measured temperature is higher than or equal to a corresponding preset maximum local value, i.e. at one and the same position within the spatial distribution, the electrochemical cell is then supplied, i.e. considered, for the following steps of the determining method.

The set-point temperature may be defined so that the local temperature values are below the corresponding maximum local values. The set-point temperature may comprise substantially constant local values, or even a substantially constant local temperature gradient. It may have local values that are not constant within the spatial distribution but that remain below these preset maximum values. It may also have a local gradient that is not constant within the spatial distribution but that remains below the preset maximum values.

The measurement of the spatial distribution of the first thermal quantity may be an experimental measurement carried out on a considered electrochemical cell, which will have been manufactured beforehand, or a numerical measurement carried out on a numerical model of the considered electrochemical cell. The first thermal quantity may be the local flow rate of head-transfer fluid flowing through a cooling circuit of a bipolar plate.

The estimation of the spatial distribution of the second thermal quantity may include:

-   -   a phase of generating a mesh, for example a two-dimensional or         three-dimensional mesh, of a cooling circuit of at least one         bipolar plate of the electrochemical cell, through which circuit         a head-transfer fluid is intended to flow; and     -   a phase of simulating numerically by computer the second thermal         quantity on said mesh, by solving a discrete numerical model         expressing the second thermal quantity as a function of the         local temperature and of the first thermal quantity.

In this case, the numerical model takes into account the spatial distribution of the set-point temperature and the spatial distribution measured beforehand of the first thermal quantity. The discrete numerical model, which is what is called an electrochemical model, may be a relationship expressing a parameter representative of the local production of heat, for example the local heat flux, as a function of local temperature and of a parameter representative of the local removal of heat, for example the local flow rate of the heat-transfer fluid.

Thus, the electrochemical cell, the spatial distribution of the parameter of interest of which was obtained by the determining method, has in operation a spatial distribution of temperature substantially equal to that of the set-point temperature. Thus, the generation of unwanted new hot points or new temperature nonuniformities that could have appeared if the spatial distribution of the parameter of interest were determined using an essentially thermal approach, i.e. an approach based on a comparison of the actual temperature of hot points or nonuniformities and the set-point temperature, is avoided.

Preferably, the bipolar plates are formed from two sheets that are bonded to each other, each sheet including embossments forming, in what is called an external face, a circuit for distributing a reactive species, the embossments of the sheets together forming, in what are called internal faces that are opposite the external faces, a cooling circuit including cooling channels that communicate fluidically with one another between an inlet and an outlet of the cooling circuit. The external faces of the sheets are oriented toward an electrochemical-cell electrode. The cooling channels communicate fluidically with one another in the sense that, between the inlet and the outlet of the cooling circuit, they form a two-dimensional fluidic network, i.e. a non-linear network.

Preferably, the step of determining the spatial distribution of the parameter of interest is carried out also depending on a preset value of a parameter representative of the overall electrical power of the electrochemical cell. This parameter may be the overall electric power, namely the product of the voltage and current density measured across the terminals of the cell, or even the efficiency thereof, for example the voltage of the cell for a given current density. It is then possible both to manage the local temperature within the electrochemical cell, with the aim of optimizing the lifetime thereof, and to maintain a wanted electrical power.

The first thermal quantity is preferably an effective local temperature measured within the cell in operation; and the second thermal quantity is then a quantity representative of a local difference between the effective temperature and the set-point temperature.

Preferably, step v) includes:

-   -   a sub-step of calculating a spatial distribution of a         correctional coefficient from the spatial distribution of the         second thermal quantity; and     -   a sub-step in which the spatial distribution of the parameter of         interest is determined by correlating the initial spatial         distribution of the parameter of interest with the spatial         distribution of the correctional coefficient.

Preferably, step v) includes:

-   -   a sub-step of identifying at least one zone Z_(i) of the cell in         which the second thermal quantity has an estimated local value         above a preset threshold value;     -   a sub-step of determining the spatial distribution of the         parameter of interest by modifying the initial spatial         distribution in the identified zone Z_(i) depending on the         estimated local value of the second thermal quantity in this         zone.

Preferably, the first thermal quantity is representative of the local removal of the heat produced by the cell in operation, and the second thermal quantity is representative of the local production of heat by the cell in operation.

Preferably, the first thermal quantity is the measured effective local flow rate of a heat-transfer fluid flowing in a cooling circuit of a bipolar plate of the cell, and the second thermal quantity is the local heat flux produced by the cell in operation.

Preferably, step v) includes:

-   -   a first sub-step of estimating a spatial distribution of the         density of an electrical signal produced by the cell in         operation, from said estimated spatial distribution of the         produced heat flux; and     -   a second sub-step of determining the spatial distribution of the         parameter, of interest, from said spatial distribution of the         density of the electrical signal.

The invention also relates to a method for producing an electrochemical-cell electrode, including steps of:

-   -   considering a reference electrochemical cell, said cell         including two electrodes separated from each other by an         electrolyte and placed between two bipolar plates suitable for         bringing reactive species to the electrodes and for removing the         heat produced by the cell in operation, at least one electrode         including a diffusion layer suitable for ensuring the diffusion         of a reactive species as far as the electrolyte, the diffusion         layer having a parameter of interest representative of a         permeability spatially distributed with an initial distribution;     -   determining a spatial distribution of the permeability         parameter, using the determining method according to any one of         the preceding features; and     -   producing said electrode, so that the permeability parameter of         the diffusion layer thereof has the determined spatial         distribution.

The step of producing said electrode may include depositing a sealant in at least one zone of the diffusion layer identified beforehand from said determined spatial distribution of the permeability parameter.

The deposited sealant may be suitable for decreasing a porosity of the diffusion layer in said zone.

The sealant may be deposited by screen printing by means of a screen-printing screen including a plurality of obturated apertures outside of said zone.

The invention also relates to an electrochemical-cell electrode including a diffusion layer and an active layer located on a first side of the diffusion layer, the diffusion layer being suitable for ensuring fluidic diffusion between the active layer and a second side opposite the first, wherein it has a parameter representative of a permeability of the diffusion layer that has a local value that varies over the area of the electrode.

The parameter representative of the permeability of the diffusion layer may be the porosity thereof, the diffusion layer having a local porosity value in at least one zone of the layer below the mean value of the porosity outside of said zone.

The diffusion layer may include a sealant in at least one zone of the layer, said sealant being suitable for locally decreasing the porosity of the layer.

The invention also relates to a method for producing an electrochemical cell, including the following steps of:

-   -   considering a reference electrochemical cell, said cell         including two electrodes separated from each other by an         electrolyte and placed between two bipolar plates suitable for         bringing reactive species to the electrodes and for removing the         heat produced by the cell in operation, at least one electrode         including a diffusion layer suitable for ensuring the diffusion         of a reactive species as far as the electrolyte, the diffusion         layer having a parameter of interest representative of a         permeability spatially distributed with an initial distribution;     -   determining a spatial distribution of the parameter of interest,         using the determining method according to any one of the         preceding features; and     -   producing the electrochemical cell, on the basis of the         reference electrochemical cell in which the parameter of         interest has the determined spatial distribution.

By “on the basis of”, what is meant is that the produced electrochemical cell has the same electrochemical properties as those of the reference cell, with the exception of the parameter of interest, which is distributed with the determined spatial distribution. The produced electrochemical cell may be the reference cell in which the initial spatial distribution of the parameter of interest has been modified to be substantially equal to the determined spatial distribution.

The invention also relates to a data storage medium containing instructions for implementing the determining method according to any one of the preceding features, these instructions being executable by a processor.

BRIEF DESCRIPTION OF THE DRAWINGS

Other aspects, aims, advantages and characteristics of the invention will become more clearly apparent on reading the following detailed description of preferred embodiments thereof, which description is given by way of nonlimiting example and with reference to the appended drawings, in which:

FIG. 1a is a schematic cross-sectional representation of an exemplary electrochemical cell, and FIG. 1b is a schematic representation illustrating the correlational relationship between the spatial distribution of heat production and the spatial distribution of heat removal the result of which is the spatial distribution of the temperature of the electrochemical cell in operation;

FIG. 2 is a flowchart of a method for determining the spatial distribution of the electrical resistance of the electrochemical cell according to a first embodiment;

FIG. 3 is a flowchart of a method for determining the spatial distribution of the electrical resistance of the electrochemical cell according to a second embodiment;

FIG. 4 is an example of a mesh of the cooling circuit, in which each mesh cell includes a local heat production term Q_(i,j) ^(e), a local heat removal term D_(i,j) ^(r), and a temperature T_(i,j) ^(c);

FIG. 5a is an exemplary spatial distribution of the effective temperature of a reference electrochemical cell in operation, for which cell the permeability of the diffusion layers of the electrodes is spatially uniform, and FIG. 5b is an exemplary spatial distribution of the effective temperature of an electrochemical cell for which the permeability of the diffusion layers has a spatial distribution determined using the method of the first embodiment.

DETAILED DESCRIPTION OF PARTICULAR EMBODIMENTS

In the figures and in the rest of the description, references that are the same represent identical or similar components. Moreover, the various embodiments and variants are not mutually exclusive and can be combined with one another. Unless indicated otherwise, the terms “substantially”, “about” and “of the order of” mean to within 10%.

The various embodiments and variants will be described with reference to a fuel cell and in particular to a PEM (proton exchange membrane) hydrogen fuel cell the cathode of which is supplied with oxygen and the anode of which with hydrogen. However, the invention is applicable to any type of fuel cell, and in particular to those operating at low temperatures, i.e. temperatures below 200° C., and to electrochemical electrolyzers.

FIG. 1a partially and schematically illustrates an exemplary electrochemical cell 1 belonging to a stack of cells of a PEM fuel cell. The cell 1 includes an anode 10 and a cathode 20 that are separated from each other by an electrolyte here comprising a polymer membrane 30, the electrodes 10, 20 being placed between two bipolar plates 40, 50 that are suitable for bringing reactive species to the electrodes and for removing the heat produced during the electrochemical reaction.

The bipolar plates include a circuit 41 for distributing hydrogen, which circuit is located on an anodic side, and a circuit 51 for distributing oxygen, which circuit is located on a cathodic side. They are here formed from two metal sheets 2 a, 42 b; 52 a, 52 b, that are joined to one another by welded zones or spot welds and pressed so as to form the distributing circuits. The arrangement of the embossments also allows a cooling circuit 43, 53 to be produced inside the plates, through which a heat-transfer fluid may flow without making contact with the electrodes. Other bipolar-plate technologies may be used, for example the plates may be produced from a filled composite, for example a composite filled with graphite, the embossments of which are produced by molding.

Each electrode 10, 20 includes a gas diffusion layer (GDL) 11, 21 placed in contact with one of the bipolar plates 40, 50 and an active layer 12, 22 located between the membrane 30 and the diffusion layer 11, 21. The active layers 12, 22 are the site of electrochemical reactions. They include materials allowing the oxidation and reduction reactions at the respective interfaces of the anode and cathode with the membrane to take place. More precisely, they may include a catalyst, for example platinum particles, placed on an electrically conductive support, for example a carbon-containing matrix, and an ionomer ensuring the protonic conductivity, Nafion for example. The diffusion layers 11, 21 are made from a porous material that permits the diffusion of the reactive species from the distributing circuit of the bipolar plates to the active layers, and the diffusion of the products generated by the electrochemical reaction to the same distributing circuit. They have a given porosity φ that defines a permeability k.

The porosity φ of a diffusion layer is defined as the ratio of the volume of the pores of the porous material to the total volume of the material. It is conventionally comprised between 10% and 90%, and is generally about 80%. The permeability k represents the capacity of the layer to let a fluid pass through under the effect of a pressure gradient, such as expressed by Darcy's law:

$\begin{matrix} {\overset{\rightarrow}{\nabla P} = {{- \frac{\mu}{k}}\overset{\rightarrow}{U}}} & (1) \end{matrix}$

where {right arrow over (ΔP)} is the pressure gradient, μ the viscosity of the fluid, k the permeability of the diffusion layer and {right arrow over (U)} the Darcy velocity, which depends on flow rate and on cross-sectional area perpendicular to the flow.

FIG. 1b schematically shows the spatial distribution of the temperature T of the electrochemical cell as the resultant of a correlational relationship between the spatial distribution of a heat production source term, in other words a quantity representative of the production of heat by the cell, such as the produced heat flux Q, and the spatial distribution of a quantity representative of the removal of the heat produced, for example the mass flow rate D of the heat-transfer fluid in the cooling circuit.

Thus, contrary to the teaching of the prior-art document cited above, it is not enough to increase the uniformity of the distribution of production of heat Q and therefore of the distribution of the heating of the cell to make the distribution of the effective temperature T of the cell uniform. Specifically, it is important to take into account both the possible presence of local nonuniformities in the heat-production term Q and the possible presence of local nonuniformities in the heat-removal term D.

The local production of heat, or more precisely the local produced heat flux Q, is directly proportional to the local electrical power production, or more precisely to the local current density I, as expressed by the relationship between their respective spatial distributions:

Q _(x,y) =I _(x,y) (ΔH/2F−U _(x,y))   (2)

where ΔH is the enthalpy of the electrochemical reaction, F is Faraday's constant, and U_(x,y) is the spatial distribution of the local voltage of the cell, the enthalpy and voltage possibly being considered to be almost uniform at every point of the cell. Thus, the production of heat is impacted by any nonuniformity due to fluidic parameters (dimensions of the circuits for distributing reactive species, etc.), electrochemical parameters (local properties of the electrodes and of the membrane, etc.) but also electrical parameters (electrical resistances of the various components of the cell, the resistivities of the materials for example and the contact resistances between the components of the cell, etc.), which parameters all influence the current-density distribution.

The removal of heat via the flow of heat-transfer fluid may also exhibit local nonuniformities especially due to minor head losses in the cooling circuit. These head losses are a result of the dimensions of the cooling circuit as produced during the production of the bipolar plates, and may lead to the formation of zones of high flow rate or of low flow rate within the cooling circuit.

In the context of the invention, it is sought to adapt the spatial distribution of a parameter of interest influencing the production of electrical power, and therefore of thermal energy, so that the spatial distribution of the effective temperature of the cell in operation corresponds to that of a set-point temperature, while taking into account the spatial distribution of the effective heat removal that the electrochemical cell exhibits.

The parameter influencing the production of electrical power is here a parameter representative of the permeability of the diffusion layer of at least one electrode of the electrochemical cell. The value of this parameter of interest influences current density I_(x,y) locally insofar as it determines the amount of reactive species able to diffuse locally as far as the active layer. The parameter of interest may thus be the permeability k, which is defined as the capacity of a porous medium to be passed through by a fluid under the effect of a pressure gradient, and which is expressed in darcies or in m². It may also be a question of any equivalent parameter, such as porosity φ, a permeability coefficient K defined as the ratio of the permeability k to the viscosity μ of the fluid, or a fluidic diffusion coefficient. It will be noted that the relationship between permeability and porosity is especially expressed by the Kozeny-Carman equation (see for example Feser et al., Experimental characterization of in-plane permeability of gas diffusion layers, Journal of Power Sources, 162 :1226-1231, 2006). It will be understood here that the lower the local permeability (for example because of a low porosity), the lower the speed with which reactive species pass through the diffusion layer and hence the lower the amount of reactive species able to reach the active layer. This results in a decrease in the local current density exchanged by the cell and therefore in the local produced heat flux. Conversely, the higher the local permeability (especially because of a high porosity), the higher the speed and therefore the amount of reactive species able to reach the active layer. This therefore leads to an increase in the local current density exchanged by the cell and therefore in the local produced heat flux.

By the temperature of the cell, what is meant is local temperature, i.e. the spatial distribution of the temperature of any one of the components of the cell, for example one of the bipolar plates or even one of the electrodes. The temperature of the cell may thus correspond to the spatial distribution of the temperature of the heat-transfer fluid in the cooling circuit. The effective temperature of the cell is the spatial distribution of the temperature of the cell in operation, at the polarization point defined by the voltage of the cell U_(tot) and the current I_(tot), i.e. the local current density I_(x,y) integrated over the entire area of the cell.

By parameter representative of heat removal, what is meant is a parameter the value of which represents the capacity of the cell to remove locally produced heat. It may in particular be a question of the local mass or volume flow rate of the heat-transfer fluid flowing in the cooling circuit.

By spatial distribution of a parameter, what is meant is the local value of this parameter at every point in the cell, or more precisely, at every point (x,y) in a plane parallel to the cell in the what is called active zone corresponding to the areal extent of the active layers of the electrodes.

Thus, an electrochemical cell the permeability of which is spatially distributed with the distribution thus determined will have an effective temperature, or temperature during operation of the cell, substantially equal to the set-point temperature. This set-point temperature advantageously has a spatial distribution that is substantially uniform scalarwise or gradientwise. By uniform scalarwise, what is meant is that the local value of the temperature is substantially constant. By uniform gradientwise, what is meant is that the local temperature gradient is substantially constant. The local temperature values may however not be constant while remaining below preset maximum local values. The cell then does not contain zones of excess temperature, or hotspots, that on the one hand may increase the rate of the degradation reactions of the components of the cell, and on the other hand may generate mechanical stresses liable to degrade the mechanical strength of the components of the cell. The lifetime of the electrochemical cell is then preserved. By hotspot, what is for example meant is a zone of the cell that contains a temperature peak or a temperature-gradient peak. More precisely, a hotspot may be a zone where the difference between the local temperature and the inlet temperature of the cooling circuit is larger than the product of a coefficient and the temperature difference between the inlet and outlet of the cooling circuit, the coefficient possibly being about 1.2 to 3 or more, and preferably being about 1.5. By way of example, for a temperature of 77° C. at the inlet of the cooling circuit and of 80° C. at the outlet of the circuit, and for a coefficient equal to 1.5, a hotspot is a zone of the cell in which the local temperature exceeds 81.5° C.

FIG. 2 is a flowchart of a method for determining the spatial distribution of the parameter of interest representative of the permeability of an electrode, according to a first embodiment. In this example, the parameter of interest is the permeability k of a diffusion layer of an electrode of the cell, for example the cathodic diffusion layer, the value k_(x,y) of which has a direct influence on the local electrical current density I_(x,y) exchanged locally during the electrochemical reaction and therefore on the local produced heat flux Q_(x,y).

Generally, according to this first embodiment, an optimized spatial distribution k_(x,y) ^(f) of the permeability k is determined from an estimation of the spatial distribution ΔT_(x,y) ^(e) of a difference ΔT^(e) between an effective temperature T^(r) of the cell in operation—in which cell the permeability is spatially distributed with a given initial distribution—and a preset set-point temperature T^(c). It is then possible to modify the permeability k of the diffusion layer so that it has the optimized distribution k_(x,y) ^(f), so that the effective temperature T^(r) of the modified cell is substantially equal to the set-point temperature T^(c).

In a first step 110, a reference electrochemical cell is defined within which the permeability k of the cathodic diffusion layer is spatially distributed with an initial distribution k_(x,y) ^(f). The cell has a structure identical or similar to that described with reference to FIG. 1. The initial spatial distribution k_(x,y) ^(f) of the permeability k may be substantially uniform, i.e. here it has a value that is substantially constant at every point in the active zone.

In a step 120, a spatial distribution T_(x,y) ^(c) of a set-point temperature T^(c) of the reference cell when the latter is in operation and producing a total current density I_(tot) for a given voltage U_(tot) is defined. To the first order, the set-point temperature T^(c) of the cell may correspond to a temperature of the heat-transfer fluid in the cooling circuit, the distribution of this temperature then especially depending on its values at the inlet T_(e) ^(c) and outlet T_(s) ^(c) of the cooling circuit. By way of illustration, the inlet temperature may be set beforehand, for example to 75° C., and the outlet temperature may be estimated from the thermal power P_(th) to be removed, the latter corresponding to the electrical power P_(e)=I_(tot).U_(tot) delivered during operation of the cell. The thermal power P_(th) is estimated by integrating over the active zone the local produced heat flux Q_(x,y) obtained from relationship (2). The outlet temperature T_(s) ^(c) is then estimated by correlating the thermal power P_(th) estimated beforehand with the average total flow rate <D_(tot)> of the heat-transfer fluid in the cooling circuit, by means of the heat capacity c_(p) of the heat-transfer fluid. It is then possible to define the spatial distribution T_(x,y) ^(c) of the set-point temperature T^(c) from the values of the temperature of the heat-transfer fluid at the inlet T_(e) ^(c) and outlet T_(s) ^(c) of the cooling circuit, the distribution T_(x,y) ^(c) advantageously being uniform gradientwise, i.e. the local set-point temperature gradient is substantially constant.

In a step 130, a spatial distribution T_(x,y) ^(r) of a first thermal quantity representative of the temperature of the cell in operation is obtained. The first thermal quantity is here the effective temperature T^(r) of the electrochemical cell when it is operating under the same operating conditions as those considered in step 120. This distribution T_(x,y) ^(r) is not estimated but is the result of a measurement by experimental or numerical means. It may thus be obtained by experimental measurement of an electrochemical cell having the same properties as the reference cell defined in step 110, for example by means of an S++ board sold by “S++ Simulation Services”, including an invasive plate inserted between two bipolar plates and suitable for measuring a spatial distribution of temperature. The distribution T_(x,y) ^(r) of effective temperature may also be obtained by numerical simulation using an electrochemical cell model, for example that described in the publication by Robin et al., Development and experimental validation of a PEM fuel cell 2D model to study heterogeneities effects along large area cell surface, International Journal of Hydrogen, 40, 2015, 10211-10230, or even the model described in the publication by Inoue et al. Numerical analysis of relative humidity distribution in polymer electrolyte fuel cell stack including cooling water, J. Power Sources 162 (2006) 81-93.

The distribution T_(x,y) ^(r) of the effective temperature T^(r) obtained by experimental or numerical measurement thus takes into account local nonuniformities in the produced heat flux, which depends on local current density, and local nonuniformities in heat removal, which especially depends on the local flow rate of the heat-transfer fluid in the cooling circuit.

In a step 140, the spatial distribution of a second thermal quantity is estimated, here a quantity ΔT^(e) representative of a local difference between the effective temperature T^(r) and the set-point temperature T^(c). This quantity of local difference ΔT^(e) is estimated from the spatial distribution T_(x,y) ^(c) of the set-point temperature T^(c) defined in step 120 and from the spatial distribution T_(x,y) ^(r), of the effective temperature T^(r) measured in step 130. It may be a question of the difference between the local value of the effective temperature and that of the set-point temperature, or of a ratio of these values, inter alia. Here, the term-to-term difference between the distributions of the effective temperature and set-point temperature are considered: ΔT_(x,y) ^(e)=T_(x,y) ^(r)−T_(x,y) ^(c).

Next, in a step 150, the spatial distribution k_(x,y) ^(f) of the permeability parameter of interest k is determined depending on the spatial distribution ΔT_(x,y) ^(e) of the local difference ΔT^(e).

According to a first variant, a correctional coefficient is firstly calculated, the spatial distribution of which is proportional term-to-term to that ΔT_(x,y) ^(e) of the local difference ΔT^(e). By way of example, the correctional coefficient varies continuously between a minimum value and a maximum value, as the local difference varies between a substantially zero value and a maximum value, respectively. The minimum value of the correctional coefficient may here be substantially comprised between 0 and 0.75, or even between 0 and 0.5, and for example be substantially equal to 0, 0.1, 0.2 or 0.3, and the maximum value may be substantially equal to unity. Next, the spatial distribution k_(x,y) ^(f) of the permeability k may be determined by correlation, for example by a term-to-term multiplication, of the initial spatial distribution k_(x,y) ^(i) of the permeability k with the spatial distribution of the correctional coefficient. Thus, in the zones of the cell where the difference ΔT^(e) between the effective temperature and the set-point temperature has a maximum value, i.e. in the zones called hotspots, the initial local value k_(x,y) ^(f) of the permeability k is multiplied by the local value of the correctional coefficient, which is for example equal to 0.25 or even less. Thus, the permeability has a new local value that is decreased with respect to the initial local value, thereby decreasing the amount of reactive species able to diffuse as far as the active layer, thereby leading to a decreased local current density and therefore a decreased produced heat flux.

According to a second variant, firstly at least one zone Z_(i) of the cell in which the difference ΔT^(e) has a value above a preset threshold value is identified, the threshold value for example being representative of a hotspot. Next, the spatial distribution k_(x,y) ^(f) of the permeability k is determined by modifying the initial spatial distribution k_(x,y) ^(i) in the identified zone Z_(i) depending on the local value of the difference ΔT^(e) in this zone. By way of example, the initial spatial distribution k_(x,y) ^(i) may be modified locally using a correctional coefficient the value of which is proportional to that of the difference ΔT^(e) in this zone. As in the first variant, the correctional coefficient varies continuously between a minimum value and a maximum value, for example between 0.25 and 1.

Thus, a spatial distribution k_(x,y) ^(f) of the permeability k of the diffusion layer is obtained. It is then possible to modify the initial distribution k_(x,y) ^(f) of the permeability k of the diffusion layer of the cathode of the reference cell so that it is the same as the new distribution determined in step 150. The cell thus optimized then has, in operation, an effective temperature the spatial distribution of which is substantially equal to that of the set-point temperature. Insofar as the distribution of the set-point temperature is advantageously uniform, the cell in operation has an effective temperature the distribution of which is also substantially uniform, thus allowing the lifetime of the cell to be preserved.

FIG. 3 is a flowchart of a method for determining the spatial distribution of a parameter of interest representative of the permeability of a diffusion layer of at least one electrode of an electrochemical cell, according to a second embodiment. In this example, the parameter of interest is the permeability k of the diffusion layer, here the cathode, the value of which has a direct influence on the electrical current density produced locally during the electrochemical reaction.

Generally, according to this second embodiment, the spatial distribution k_(x,y) ^(f) of the permeability k is determined from the estimation of the spatial distribution of the production of heat necessary to obtain the spatial distribution of a set-point temperature, while taking into account the spatial distribution of a thermal quantity representative of the effective heat removal in the cell. It is then possible to modify the initial distribution of the permeability of the diffusion layer so that it has an optimized spatial distribution, so that the effective temperature is then substantially equal to the set-point temperature. The electrochemical cell, the parameter of interest of which is spatially distributed with the optimized distribution, has in operation a temperature substantially equal to the set-point temperature. Unwanted new hotspots or new temperature nonuniformities are not formed.

This approach, which is what may be referred to as an electrochemical and no longer essentially thermal approach, is particularly advantageous when at least one bipolar plate, or even both bipolar plates, of the electrochemical cell are formed from sheets that are bonded to one another and that contain embossments that define a two-dimensional cooling circuit. The embossments of each sheet, in the faces referred to as the external faces of the sheets, i.e. the faces oriented toward an electrode, define a circuit for distributing reactive species. In the internal faces, i.e. the faces opposite the external faces, the embossments form a cooling circuit through which a heat-transfer fluid is intended to flow. The cooling circuit is what is called linear when the cooling channels do not communicate with one another, i.e. when the heat-transfer fluid, between the inlet and outlet of the cooling circuit, cannot substantially pass from one cooling channel to another. The cooling circuit is what is called two-dimensional when the cooling channels communicate with one another, so as to form a two-dimensional fluidic network that is non-linear. This is especially the case when the distributing channels of a sheet are not parallel to those of the other sheet.

In a first step 210, a reference electrochemical cell is defined, or supplied, within which the permeability k of the cathodic diffusion layer is spatially distributed with an initial distribution k_(x,y) ^(f). The initial spatial distribution k_(x,y) ^(f) of the permeability k may be substantially uniform scalarwise, so that its local value is substantially constant at every point in the active zone. The cell has a structure that is identical or similar to that described with reference to FIG. 1 and this step is similar or identical to the step 110 described above. The considered electrochemical cell then has, in operation, a spatial distribution of temperature at least one local value of which is higher than or equal to a preset maximum local value. The latter may be constant or differ depending on the considered point of the electrochemical cell. This step may include:

-   -   a phase of experimentally prototyping or numerically modeling an         electrochemical cell;     -   a phase of measuring the spatial distribution of the temperature         within the electrochemical cell in operation; then     -   a phase of comparing the measured spatial distribution of the         temperature to a preset spatial distribution of a maximum         temperature. The local values of this spatial distribution of         maximum temperature are the what are called preset maximum local         values.

When at least one local value of the measured temperature is higher than or equal to a corresponding preset maximum local value, i.e. at one and the same position within the spatial distribution, the electrochemical cell is then supplied, i.e. considered, for the following steps of the determining method.

In a step 220, a spatial distribution T_(x,y) ^(c) of a set-point temperature T^(c) of the reference cell when the latter is in operation and producing a total current density I_(tot) for a given voltage U_(tot) is defined. This step is similar or identical to the step 120 described above. The local values of the spatial distribution of the set-point temperature are lower than corresponding maximum local values.

Optionally, it is advantageous to specify the spatial distribution T_(x,y) ^(c) of the set-point temperature T^(c) as a function of the spatial distribution of the concentration of reactive species in the active zone between the inlet and outlet of the corresponding distributing circuit. Specifically, the consumption of reactive species within the active zone of the cell leads to a gradual decrease in the concentration of reactive species along the distributing circuit. This gradual decrease results in a decrease in the local current density produced by the cell and therefore in the local production of heat, thereby leading to the formation of nonuniformities in the temperature of the cell. To compensate for this gradual decrease in the production of heat, it is advantageous to define a set-point temperature that takes into account the decrease in the concentration of reactive species, so that the effective temperature of the cell in operation corresponds to the set-point temperature, the latter advantageously having a uniform spatial distribution. To do this, the spatial distribution {tilde over (T)}_(x,y) ^(c) of the specified set-point temperature {tilde over (T)}^(c) may for example be written:

{tilde over (T)} _(x,y) ^(c) =T _(x,y) ^(c) +K ^(i).[max(c _(x,y) ^(i))−c _(x,y) ^(i)]  (3)

where c_(x,y) ^(i) is the spatial distribution of the concentration c^(i) in reactive species i, for example in oxygen, and K^(i) is a positive constant, for example close to 1, which may be subsequently adjusted. The spatial distribution c_(x,y) ^(i) of the concentration may be estimated to the first order from the routing of the channels of the distributing circuit of the reactive species in question and by assuming a uniform consumption throughout the active zone. It may also be more accurately determined by numerical or experimental measurement of the spatial distribution of the current density in a cell that is similar or identical to the reference cell, which allows the spatial distribution of the concentration of the reactive species to be deduced. Other relationships (3) may be used to specify the spatial distribution of the set-point temperature while taking into account the spatial variation in the concentration of reactive species. Thus, a spatial distribution {tilde over (T)}_(x,y) ^(c) of the set-point temperature {tilde over (T)}^(c) is obtained that thus allows a distribution of the effective temperature of the cell to be obtained the uniformity of which is improved.

Moreover, optionally and possibly complementarily with the step of specifying the set-point temperature described above, it is advantageous to specify the spatial distribution T_(x,y) ^(c) of the set-point temperature T^(c) as a function of the spatial distribution φ_(x,y) of the relative humidity φ in the distributing circuits. The relative humidity φ is defined conventionally as the ratio of the partial pressure P_(H2O) of the water vapor contained locally in the gas flowing through the distributing circuit to the saturated vapor pressure P_(sat). The relative humidity φ has an effect on the electrochemical response. Thus, to compensate for the local variation in relative humidity, it is advantageous to define a set-point temperature that compensates for this local variation, for example for local humidification or dehumidification of the pores of the diffusion layers, so that the effective temperature of the cell in operation has a uniform spatial distribution. To do this the spatial distribution {tilde over (T)}′_(x,y) ^(c) of the specified set-point temperature {tilde over (T)}′^(c) may for example be written:

{tilde over (T)}′_(x,y) ^(c)=T_(x,y) ^(c)+K^(φ).[φ_(x,y)/φ_(in)]  (4)

where φ_(x,y) is the spatial distribution of the relative humidity φ in the distributing circuit, φ_(in) is the relative humidity at the inlet of the distributing circuit, and K^(φ) is a positive constant, for example close to 1, which may be subsequently adjusted. The distribution φ_(x,y) of the relative humidity φ may be estimated to the first order from the routing of the channels of the distributing circuit in question and by assuming a uniform current density throughout the active zone. It may also be more accurately determined by numerical or experimental measurement of the spatial distribution of the current density in a cell that is similar or identical to the reference cell, which allows the spatial distribution of the relative humidity to be deduced. Other relationships (4) may be used to specify the spatial distribution of the set-point temperature from the spatial variation in relative humidity. Thus, a spatial distribution {tilde over (T)}_(x,y) ^(c) of the set-point temperature {tilde over (T)}^(c) is obtained that thus allows a distribution of the effective temperature of the cell to be obtained the uniformity of which is improved.

In a step 230, a spatial distribution D_(x,y) ^(r) of a first thermal quantity representative of the removal of heat D^(r) within the cell in operation is obtained. The first thermal quantity is here the mass flow rate D^(r) of heat-transfer fluid in the cooling circuit. This distribution D_(x,y) ^(r) is not estimated but is the result of a measurement by experimental or numerical means. It may thus be obtained by experimental measurement of an electrochemical cell having the same properties as the reference cell defined in step 210, for example by means of a particle image velocimetry (PIV) technique or any other suitable technique, carried out on a cooling circuit having the same dimensional characteristics as that of the reference cell. The distribution D_(x,y) ^(r) of the mass flow rate D^(r) may also be obtained by numerical simulation using a flow simulation software package such as FLUENT or COMSOL for example.

In a step 240, the spatial distribution Q_(x,y) ^(e) of a second thermal quantity Q^(e) is estimated from said spatial distribution T_(x,y) ^(c) of the set-point temperature T^(c) defined in step 220 and from said spatial distribution D_(x,y) ^(r) of the heat-transfer fluid flow rate D^(r) obtained in step 230. The second thermal quantity is representative of the local production of heat and here corresponds to the local heat flux Q^(e) that the heat-transfer fluid removes D^(r) to obtain the set-point temperature T^(c).

To do this, as illustrated in FIG. 4, the cooling circuit is discretized into a two-dimensional or three-dimensional, here two-dimensional, mesh each mesh cell of which is an elementary volume (i,j) passed through by the heat-transfer fluid. Thus, each mesh cell (i,j) of the distributing circuit has two known quantities: the local set-point temperature T_(i,j) ^(c) and the local flow rate D_(i,j) ^(r) of the heat-transfer fluid; and a quantity to be determined: the local produced heat flux Q_(i,j) ^(e). Next, the amount of heat and fluid transferred between the mesh cell in question and the adjacent mesh cells is calculated by determining, on the one hand, the temperature differences and, on the other hand, the flow rates of the heat-transfer fluid at the four facets of the mesh cell in question. This calculation may be carried out by numerical simulation by computer, on said mesh. This amounts to solving a discrete numerical model expressing the second thermal quantity, namely here the local heat flux, as a function of local temperature and of the first thermal quantity, namely here the local flow rate of the heat-transfer fluid. The numerical model, which is what is referred to as an electrochemical model, may be expressed by relationship (7).

The temperature differences at the four facets of the mesh cell (i,j) may be calculated in the following way:

δT _(i,j) ¹ =T _(i,j) ^(c) −T _(i,j+1) ^(c)   (5-1)

δT _(i,j) ² =T _(i,j) ^(c) −T _(i−1,j) ^(c)   (5-2)

δT _(i,j) ³ =T _(i,j) ^(c) −T _(i+1,j) ^(c)   (5-3)

δT _(i,j) ⁴ =T _(i,j) ^(c) −T _(i,j−1) ^(c)   (5-4)

The flow rates of the heat-transfer fluid at the four facets of the mesh cell (i,j) may be obtained by predicting the mass flow rate D_(i,j) ^(r) (here a vectorial datum) onto the vectors e_(x) and e_(y) passing through the mesh cells (i−1,j), (i,j) and (i+1,j), and through the mesh cells (i,j−1), (i,j) and (i,j+1), respectively:

d _(i,j) ¹=(D _(i,j) ^(r) .e _(y) +D _(i,j+1) ^(r) .e _(y))/2   (6-1)

d _(i,j) ²=(D _(i,j) ^(r) .e _(x) +D _(i−1,j) ^(r) .e _(x))/2   (6-2)

d _(i,j) ³=(D _(i,j) ^(r) .e _(x) +D _(i+1,j) ^(r) .e _(x))/2   (6-3)

d _(i,j) ⁴=(D _(i,j) ^(r) .e _(y) +D _(i,j−1) ^(r) .e _(y))/2   (6-4)

By convention, the local flow rate d_(i,j) is considered to be positive when the fluid enters into the mesh cell (i,j) and negative when the fluid exits therefrom.

Lastly, the spatial distribution Q_(x,y) ^(e) of the heat flux Q^(e) produced by the cell is calculated from the relationship:

Q _(x,y) ^(e) ≈Q _(i,j) ^(e)=Σ_(k=1) ⁴ d _(i,j) ^(k) .c _(p) .δT _(i,j) ^(k)   (7)

Thus, the spatial distribution of the heat flux Q^(e) that the cell must produce for the effective temperature distribution to correspond to that of the set-point temperature is obtained, the distribution of the effective mass flow rate of the heat-transfer fluid in the distributing circuit being known.

In a step 250, the spatial distribution k_(i,j) ^(f) of the permeability k is determined depending on the spatial distribution Q_(x,y) ^(e) of the produced heat flux Q^(e). To do this, it is possible to firstly estimate the spatial distribution of the density of an electrical signal produced by the cell in operation, for example a current density I^(e), from the estimated spatial distribution Q_(x,y) ^(e) of the produced heat flux Q^(e). Insofar as the produced heat flux Q^(e) is approximately proportional to the current density I^(e), the latter may be determined from the relationship:

$\begin{matrix} {I_{x,y}^{e} = {Q_{x,y}^{e} \cdot \frac{I_{tot}}{Q_{tot}}}} & (8) \end{matrix}$

where I_(tot) is the total current density delivered by the electrochemical cell in operation, and Q_(tot) is the total produced heat flux, which is obtained by integrating the spatial distribution Q_(x,y) ^(e) over all the active area.

Next, the new spatial distribution k_(x,y) ^(f) of the permeability k is determined from the local density of the electrical current I_(x,y) ^(e). To do this, one approach consists in determining the minimum k_(min) and maximum k_(max) values of the permeability of the cathodic diffusion layer. It may be a question of an experimental measurement of a cell sample having the same properties as those of the reference cell, or of a measurement by numerical simulation. Next, the spatial distribution k_(x,y) ^(f) is calculated, for example using the relationship:

$\begin{matrix} {k_{x,y}^{f} = {\max \left( {k_{\max},{k_{\min}\frac{I_{\max}^{e}}{I_{x,y}^{e}}}} \right)}} & (9) \end{matrix}$

where I_(max) ^(e) is the maximum value of the local current density I_(x,y) ^(e). The local permeability thus varies linearly between the minimum k_(min) and maximum k_(max) values as a function of the local value of the current density I^(e). Of course, any other law, for example a polynomial, exponential or logarithmic law, causing the local permeability to vary so that the maximum value k_(max) corresponds to a maximum local current density and vice versa, may be used. The minimum k_(min) and maximum k_(max) values may be preset depending on the overall electric power UI wanted for the electrochemical cell, where U is the electrical voltage and I the electrical current density measured across the terminals of the cell.

Thus, a spatial distribution k_(x,y) ^(f) of the permeability k taking into account the distribution of production of electrical power I^(e) and therefore of thermal energy Q^(e), and which ensures the effective temperature of the cell in operation corresponds to the set-point temperature T^(c), has been determined, while also taking into account the effective removal D^(r) of heat by the cooling circuit. Insofar as the set-point temperature is advantageously spatially uniform, a cell at least one of the electrodes of which includes a diffusion layer the permeability k of which is distributed with the spatial distribution k_(x,y) ^(f) thus determined has, when it is operating at the polarization point U_(tot) and I_(tot), an effective temperature the spatial distribution of which is uniform.

FIG. 5a illustrates an exemplary spatial distribution of the effective temperature of an electrochemical cell in operation, in the case where the diffusion layers have a substantially uniform permeability. Three zones of excess temperature, or hotspot zones, are present. In this example, the current density is 0.5 A/cm², the pressure is 1.5 bar and the temperature of the heat-transfer fluid at the outlet of the cooling circuit is 80° C. The relative humidity is 50% at the anode and cathode. The stoichiometry is 1.5 at the anode and 1.8 at the cathode. The diffusion layer has an average thickness of 246 μm and a porosity of 0.76.

FIG. 5b illustrates the spatial distribution of the effective temperature of the same electrochemical cell in operation, in the case where at least one diffusion layer has a permeability with the spatial distribution modified according to the first embodiment of the method (FIG. 2). It will be noted that the temperature distribution is substantially uniform and does not contain zones of excess temperature.

A method for producing an electrochemical-cell electrode will now be described, here the cathode of the cell. An electrochemical cell that is identical or similar to the reference cell defined in steps 110 and 210 is considered. It includes two electrodes separated from each other by an electrolyte and placed between two bipolar plates suitable for bringing reactive species to the electrodes and for removing the heat produced by the cell in operation. The electrodes each include a diffusion layer and an active layer. The cathode here has a diffusion layer the permeability k of which is spatially distributed with an initial distribution k_(x,y) ^(f). Using the method described above with reference to FIGS. 2 and 3, a spatial distribution k_(x,y) ^(f) of the permeability of the cathodic diffusion layer is determined. Next, in a step 160 (FIG. 2) or 260 (FIG. 3), the cathode is produced in such a way that the permeability k of the diffusion layer has the determined spatial distribution k_(x,y) ^(f).

Thus, the permeability k of the diffusion layer is modified locally so as to form nonuniformities in the spatial distribution k_(x,y) with a view to correcting the nonuniformities in the effective temperature of the cell in operation with respect to a set-point temperature. By way of example, the permeability of the diffusion layer is decreased locally in zones in which the effective temperature of the cell is liable to be above the set-point temperature. Thus, since the local quantity of reactive species capable of diffusing as far as the active layer is decreased, thereby consequently decreasing the local current density and therefore the local produced heat flux. Thus, the effective temperature of the cell corresponds locally to the set-point temperature.

To achieve this, the diffusion layer is, by way of example, impregnated with a sealant in the identified zones Z_(i) of excess temperature. The sealant may comprise, by way of example, TiO₂ or colloidal silica, or even calcium carbonate. The amount of sealant impregnated locally into the diffusion layer may thus modify the porosity thereof in order thus to obtain a local permeability k_(Zi) having the desired value.

The sealant may be an ink including water, for example in an amount of 92% to 98%, PTFE, so as to obtain the hydrophobicity desired for the diffusion layer, for example in an amount of 0.5% to 3%, a dispersant, for example triton X-100, for example in an amount of 0.3%, and TiO₂, to seal the pores of the porous material of the diffusion layer and for example in an amount of 1% to 5%. The amount of sealant having impregnated the diffusion layer locally made thus decrease the porosity thereof from the initial value, for example 80%, to 20% or even less, for example 10% or 0%, thereby correspondingly impacting permeability. Thus a local decrease in the porosity of the diffusion layer from 70% to 10% has been observed to lead to a decrease of about 2° C. in the zone in question.

The sealant may be deposited on the surface of the diffusion layer of the cathode, in an identified zone Z_(i) of excess temperature, by any deposition technique known to those skilled in the art, screen printing for example. Thus, a screen-printing screen is produced that forms a mesh of through-apertures, for example of a few square centimeters area. The apertures are obturated in order to keep only certain apertures intended to ensure the deposition of the sealant in the identified zones Z_(i). Next, the screen is placed on the diffusion layer, for example on the side of the layer opposite the active layer, then the sealant is deposited on the diffusion layer through the screen-printing screen. After the screen has been removed, only the zones Z_(i) are impregnated with the sealant. The amount of sealant may be adjusted by carrying out a plurality of successive depositions in the same zones Z_(i), while ensuring that the product deposited in a preceding step has been able to infiltrate into the diffusion layer. A drying step is provided to evaporate the water of the sealant.

Thus, the diffusion layer has a permeability, or porosity, the value of which varies locally. In at least one zone Z_(i), the local value of the permeability or porosity is lower than the average value of the permeability or porosity outside this zone Z_(i).

Particular embodiments have just been described. Alternative variants and various modifications will be apparent to the person skilled in the art. 

1. Method for determining a spatial distribution (k_(x,y) ^(f)) of a parameter of interest (k) representative of a permeability of a diffusion layer of at least one electrode of an electrochemical cell, said cell including two electrodes separated from each other by an electrolyte and placed between two bipolar plates suitable for bringing reactive species to the electrodes and for removing the heat produced by the cell in operation, at least one electrode including a diffusion layer suitable for ensuring the diffusion of a reactive species as far as the electrolyte, said method comprising: i) providing an electrochemical cell, within which the parameter of interest (k) is distributed with an initial spatial distribution (k_(x,y) ^(i)) and for which the spatial distribution of a temperature within the electrochemical cell in operation has at least one local value higher than or equal to a preset maximum local value; ii) defining a spatial distribution (T_(x,y) ^(c)) of a set-point temperature (T^(c)) within said electrochemical cell in operation, said distribution being such that the local temperature values are lower than preset maximum local values; iii) measuring a spatial distribution (D_(x,y) ^(r)) of a first thermal quantity representative of the local removal of heat (D^(r)) within said electrochemical cell in operation; iv) estimating a spatial distribution (Q_(x,y) ^(e)) of a second thermal quantity (Qe) representative of the local production of heat (Qe) within said electrochemical cell in operation, depending on said spatial distribution (T_(x,y) ^(c)) of the set-point temperature (T^(c)) and on said measured spatial distribution (D_(x,y) ^(r)) of the first thermal quantity (D^(r)), so that the spatial distribution of the temperature of said electrochemical cell in operation, the first thermal quantity (D^(r)) of which cell having said measured spatial distribution (D_(x,y) ^(r)) and the second thermal quantity (Q^(c)) of which cell having said estimated spatial distribution (Q_(x,y) ^(c)), is substantially equal to that (T_(x,y) ^(c)) of the set-point temperature (T^(c)); and v) determining a spatial distribution (k_(x,y) ^(f)) of the parameter of interest (k) depending on the spatial distribution (Q_(x,y) ^(c)) of the second thermal quantity (Q^(c)).
 2. Determining method according to claim 1, wherein the bipolar plates are formed from two sheets that are bonded to each other, each sheet including embossments forming, in what is called an external face, a circuit for distributing a reactive species, the embossments of the sheets together forming, in what are called internal faces that are opposite the external faces, a cooling circuit including cooling channels that communicate fluidically with one another between an inlet and an outlet of the cooling circuit.
 3. Determining method according to claim 1, wherein determining the spatial distribution of the parameter of interest is furthermore carried out depending on a preset value of a parameter representative of an overall electrical power of the electrochemical cell.
 4. Determining method according to claim 1, wherein estimating a spatial distribution of the second thermal quantity includes: generating a mesh of a cooling circuit of at least one bipolar plate of the electrochemical cell, through which circuit a head-transfer fluid is intended to flow; and simulating numerically by computer the second thermal quantity on said mesh, by solving a discrete numerical model expressing the second thermal quantity as a function of the local temperature and of the first thermal quantity.
 5. Determining method according to claim 1, wherein the first thermal quantity is the measured effective local flow rate (D^(r)) of a heat-transfer fluid flowing in a cooling circuit of a bipolar plate of the cell, and the second thermal quantity is the local heat flux (Q^(e)) produced by the cell in operation.
 6. Determining method according to claim 5, wherein v) includes: a) estimating a spatial distribution of the density of an electrical signal (I^(c)) produced by the cell in operation, from said estimated spatial distribution of the produced heat flux (Q^(e)); and b) determining the spatial distribution of the parameter of interest (k), from said spatial distribution of the density of the electrical signal (I^(c)).
 7. Method for producing an electrochemical-cell electrode, comprising: i) considering a reference electrochemical cell, said cell including two electrodes separated from each other by an electrolyte and placed between two bipolar plates suitable for bringing reactive species to the electrodes and for removing the heat produced by the cell in operation, at least one electrode including a diffusion layer suitable for ensuring the diffusion of a reactive species as far as the electrolyte, the diffusion layer having a parameter of interest representative of a permeability (k) spatially distributed with an initial distribution (k_(x,y) ^(i)); ii) determining a spatial distribution (k_(x,y) ^(f)) of the permeability parameter (k), using the method according claim 1; and iii) producing said electrode, so that the permeability parameter (k) of the diffusion layer thereof has the determined spatial distribution (k_(x,y) ^(f)).
 8. Producing method according to claim 7, wherein producing said electrode includes depositing a sealant in at least one zone (Z¹) of the diffusion layer identified beforehand from said determined spatial distribution (k_(x,y) ^(f)) of the permeability parameter (k).
 9. Producing method according to claim 8, wherein the deposited sealant is suitable for decreasing a porosity of the diffusion layer in said zone (Z^(i)).
 10. Producing method according to claim 8, wherein the sealant is deposited by screen printing by means of a screen-printing screen including a plurality of obturated apertures outside of said zone (Z^(i)).
 11. Method for producing an electrochemical cell, comprising: considering a reference electrochemical cell, said cell including two electrodes separated from each other by an electrolyte and placed between two bipolar plates suitable for bringing reactive species to the electrodes and for removing the heat produced by the cell in operation, at least one electrode including a diffusion layer suitable for ensuring the diffusion of a reactive species as far as the electrolyte, the diffusion layer having a parameter of interest representative of a permeability (k) spatially distributed with an initial distribution (k_(x,y) ^(i)); determining a spatial distribution (k_(x,y) ^(f)) of the parameter of interest (k), using the determining method according to claim 1; and producing the electrochemical cell, on the basis of the reference electrochemical cell in which the parameter of interest (k) has the determined spatial distribution (k_(x,y) ^(f)).
 12. Data storage medium containing instructions for implementing the determining method according to claim 1, these instructions being executable by a processor.
 13. Producing method according to claim 9, wherein the sealant is deposited by screen printing by means of a screen-printing screen including a plurality of obturated apertures outside of said zone (Z¹). 